Bacterium X has a generation time of 15 minutes Starting wit

Bacterium X has a generation time of 15 minutes.

Starting with 10 cells in log phase, how long does it take to produce about 10,000 cells?

[ n = log10(NT/N0)/0.301]

Solution

Ans.

Using the formula for bacterial growth-  

ln (N2/ N1) = k (t2-t1)            - equation 1

Where, t2 = final time , t1= initial time (0 min),

N2= population at t2 (final population), N1= population at t1 (initial), k = specific growth rate

Given,

            Generation time, g = 15 minutes

Now, specific growth rate, k = (ln2 / generation time) = 0.693 / 15 min = 0.0462 min^-1

Also given

                        N1 = 10           , N2 = 10000    ; let’s initial time, t1 = 0         ; t2 = ?

Putting the values in equation 1 –

                        ln (10000 / 10) = (0.0462 min^-1) (t2-0)     

                        or, 6.9077 = (0.0462 min^-1) (t2-0)

                        or, t2 = 6.9077 / 0.0462 min^-1 = 149.51 min

Thus, the required time = 149.51 min = 2.49 hours